The present invention relates to RF transmission systems and methods, and more particularly, to peak-to-average power ratio (or crest factor) reduction in orthogonal frequency division multiplexing (OFDM) systems using blind selected pilot tone modulation.
OFDM is a spectrally efficient multicarrier modulation technique for high speed data transmission over multipath fading channels. However, OFDM signals suffer from significant amplitude fluctuations; i.e., they exhibit large peak-to-average power ratios (PARs). Crest factor is the square root of PAR so they have the same value in dB. These two terms are used interchangeably in the literature and herein. High PARs require significant backoff of the average operating power of a RF power amplifier if the signal is to be linearly amplified. Power inefficiency leads to low battery life for a mobile user and high operating cost for the base station. According to G. Rabjohn and J. Wight, in “Improving efficiency, output power with 802.11a out-phasing PAs,” CommsDesign.com (EE Times), January 2004, the high power consumption and limited performance of traditional 802.11a OFDM systems had delayed the adoption of 802.11a and dual-band WLAN products.
Denote by {Xl[k]k=0N−1} the lth block of the frequency domain OFDM signal drawn from a known constellation, where N is the number of sub-carriers. For the balance of this disclosure, the block index l will be dropped for notational simplicity, since OFDM can be free of inter-block interference with proper use of the cyclic prefix. The complex baseband OFDM signal can be written as
                                          x            ⁡                          (              t              )                                =                                    1                              N                                      ⁢                                          ∑                                  k                  =                  0                                                  N                  -                  1                                            ⁢                                                X                  ⁡                                      [                    k                    ]                                                  ⁢                                  ⅇ                                                                                    j                        ⁢                        2                        ⁢                        π                                            ⁢                                                                                          ⁢                      kt                                                              T                      s                                                                                                          ,                                  ⁢                  0          ≤          t          ≤                      T            s                                              (        1        )            where Ts is the OFDM symbol period and j=√{square root over (−1)}. The PAR of x(t) is defined by H. Ochiai, for example, in “Performance analysis of peak power and band-limited OFDM system with linear scaling,” IEEE Trans. Wireless Commun., vol. 2, no. 5, pp. 1055-1065, September 2003, as
                                          PAR            ⁡                          (                              x                ⁡                                  (                  t                  )                                            )                                =                                    P              max                                      P              av                                      ,                            (        2        )            where Pmax=max0≦l≦T|x(t)|2 is the peak power, Pav=Ē|x(t)|2 is the average power of the OFDM symbol, and E[.] denotes expectation, or time-averaged expectation if x(t) is nonstationary. Nyquist-rate sampled OFDM signal is given by x[n]=x(t)|t=nT,IN.
According to an Altera Corporation white paper entitled “Accelerating WiMAX system design with FPGAs,”, October 2004, http://www.altera.com/literature/wp/wp_wimax.pdf, crest factor reduction (CFR) is an essential function for OFDM based systems such as WiMAX (IEEE 802.16). The topic of CFR has attracted a lot of attention in the recent years. Proposed techniques include (i) distortionless CFR, such as coding discussed by A. E. Jones, T. A. Wilkinson, and S. K. Barton, in “Block coding scheme for reduction of peak to mean envelope power ratio of multicarrier transmission scheme,” Elec. Lett., vol. 30, no. 25, pp. 2098-2099, December 1994, tone reservation discussed by J. Tellado, in Multicarrier Modulation with Low PAR—Applications to DSL and Wireless, Kluwer Academic, 2000 and B. S. Krongold and D. L. Jones, in “An active-set approach for OFDM PAR reduction via tone reservation,” IEEE Trans. Signal Processing, vol. 52, issue 2, pp 495-509, February 2004, tone injection discussed by J. Tellado, in Multicarrier Modulation with Low PAR—Applications to DSL and Wireless, Kluwer Academic, 2000, selected mapping discussed by R. W. Bäuml, R. F. H. Fischer and J. B. Huber, in “Reducing the peak-to-average power ratio of multicarrier modulation by selected mapping,” Elec. Lett., vol. 32, no. 22, pp. 2056-2057, October 1996, M. Breiling, S. H. Muller-Weinfurtner, and J. B. Huber, in “SLM peak-power reduction without explicit side information,” IEEE Commun. Lett., vol. 5, no. 6, pp. 239-241, June 2001, and A. D. S. Jayalath and C. Tellambura, in “A blind SLM receiver for PAR-reduced OFDM,” in Proc. IEEE Vehicular Technology Conference—Fall, vol. 1, pp. 219-222, September 2002, and partial transmit sequence discussed by A. D. S. Jayalath and C. Tellambura, in “Adaptive PTS approach for reduction of peak-to-average power ratio of OFDM signal,” Elec. Lett., vol. 36, no. 14, pp 1226-1228, July 2000; (ii) CFR with distortion, such as deliberate clipping discussed by S. M. Ju and S. H. Leung, in “Clipping on COFDM with phase on demand,” IEEE Commun. Lett., vol. 7, no. 2, pp. 49-51, February 2003, transmit filtering discussed by S. B. Slimane, in “Peak-to-average power ratio reduction of OFDM signals using pulse shaping,” in Proc. IEEE GLOBECOM 2000, vol. 3, pp. 1412-1416, November 2000, companding approaches discussed by T. Jiang and G. Zhu, in “Nonlinear companding transform for reducing peak-to-average power ratio of OFDM signals,” IEEE Trans. Broadcast., vol. 50, no. 3, pp. 342-346, September 2004; and (iii) various combinations of the above. These methods entail different tradeoffs involving CFR capability, complexity, and information rate.
The techniques described herein relate to a selected mapping (SLM) approach which was first proposed by R. W. Bäuml, R. F. H. Fischer and J. B. Huber in “Reducing the peak-to-average power ratio of multicarrier modulation by selected mapping,” Elec. Lett. , vol. 32, no. 22, pp. 2056-2057, October 1996. SLM is distortionless and offers moderate to significant amount of CFR. Denote by φk(m) 0≦k≦N, 0≦m≦M−1, a set of M (random) phase sequences of length N each. In SLM, the phases of X[k] is rotated as described byZ(m)[k]=X[k]ejφk(m).  (3)
It is clear that Z(m)[k] and X[k] contain the same information, but their time-domain counterparts z(m)(t) and x(t) can have very different PAR values. From the Mcandidate z(m)(t) signals, z( m)(t), which has the lowest PAR, is transmitted. The index m (log2 M bits) may be transmitted as side information, which is of critical importance to the receiver for decoding and is generally protected by channel coding discussed by R. W. Bäuml, R. F. H. Fischer and J. B. Huber, in “Reducing the peak-to-average power ratio of multicarrier modulation by selected mapping,” Elec. Lett., vol. 32, no. 22, pp. 2056-2057, October 1996.
If {φk(m)} are independent identical distributed (i.i.d.) satisfying E[ejφk(m)]=0, then the best SLM performance can be achieved; the corresponding complementary cumulative distribution function (CCDF) is given byPr{PAR[z( m)(t)]>γ}=[Pr{PAR(x(t))>γ}]M.  (4)
The simplest and yet optimal phase rotation table is one that has 0 and π entries with equal probability. In that case, no multiplication is necessary in equation (3) since ej0=1 and ejπ=−1. The phase rotation table is pre-determined and is stored at both the transmitter and the receiver, so real-time optimization of the phase sequence is not necessary.
To avoid the information rate loss caused by the transmission of the optimum phase sequence index m, a few blind SLM schemes have been proposed. In a paper by M. Breiling, S. H. Muller-Weinfurtner, and J. B. Huber, entitled “SLM peak-power reduction without explicit side information,” IEEE Commun. Lett., vol. 5, no. 6, pp. 239-241, June 2001, a scrambling technique was described. A log2 M-bit binary label is inserted as a prefix to the frequency-domain OFDM signal and passed through a scrambler. Since the selected label is used in the receiver implicitly during descrambling, an erroneous reception of the label bits does not affect the error performance. In a paper by A. D. S. Jayalath and C. Tellambura, entitled “A blind SLM receiver for PAR-reduced OFDM,” in Proc. IEEE Vehicular Technology Conference—Fall, vol. 1, pp. 219-222, September 2002, a blind SLM receiver was proposed by employing a maximum likelihood (ML) decoder, which avoids the transmission of any side information. However, the complexity and the error rate of the ML decoder are rather high as we will show in the simulation section.
In OFDM, channel state information (CSI) can be acquired by modulating pilot tones onto predetermined sub-carriers; this is called pilot tone assisted modulation (PTAM), discussed by R. Negi and J. Cioffi, in “Pilot tone selection for channel estimation in a mobile OFDM system,” IEEE Trans. Consumer Electron., vol. 44, pp. 1122-1128, August 1998, and S. Ohno and G. B. Giannakis, in “Optimal training and redundant precoding for block transmissions with application to wireless OFDM,” IEEE Trans. Commun., vol. 50, no. 12, pp. 2113-2123, December 2002.
The concept of joint channel estimation and CFR was explored by M. J. Fernández-Getino García, O. Edfors and J. M. Páez-Borrallo, in “Joint channel estimation and peak-to-average power reduction in coherent OFDM: a novel approach,” Proc. IEEE Vehicular Technology Conference—Spring, vol. 2, pp. 815-819, May 2001. The “diversity” offered by the pilot phase (as opposed to the pilot location—the focal point of the present method) was exploited and the transmission of side information was assumed by García et al.
It would be desirable to have an improved selected mapping CFR technique that avoids the transmission of any side information and entails a very accurate detection scheme in the receiver.